Chris Jennings-Shaffer

Postdoctoral Researcher
University of Cologne

Contact Information - Research

I am currently a post doctoral scholar, under the mentorship of Kathrin Bringmann, at the University of Cologne. Beginning Fall of 2019, I am a visiting assistant professor at University of Denver.

Contact Information

Gyrhofstr. 8b,
The email address will soon be deactivated.

Mailing Address:
Mathematical Institute
University of Cologne
Gyrhofstr. 8b
50931 Cologne


My research interests are centered around integer partitions by q-series, modular forms, harmonic Maass forms, special functions, and combinatorics. In particular I am interested in congruences for partition functions that are not modular forms, introducing new cranks for partition functions, and studying rank functions via harmonic Maass forms. Additionally I enjoy all partition functions and q-series identities coming from Bailey pairs and Bailey's Lemma. I am a strong advocate for explicit computations for conjectures and verifications of theorems. Primarily my computations are done in Maple.

The current version of my CV in pdf format can be found here.

The majority of my articles can be found on arXiv.
Preprints and Submitted Work
  1. Some q-series Identities Extending Work of Andrews, Crippa, and Simon on Sums of Divisors Functions (with K. Bringmann)
    submitted ArXiv
  1. Unimodal Sequence Generating Functions Arising from Partition Ranks (with K. Bringmann)
    accepted for publication in Research in Number Theory ArXiv
  2. Proofs and Reductions of Various Conjectured Partition Idenitites of Kanade and Russell (with K. Bringmann and K. Mahlburg)
    accepted for publication in Journal fur die Reine und Angewandte Mathematik (Crelle's Journal) ArXiv
  3. A Note on Andrews' Partitions with Parts Separated by Parity (with K. Bringmann)
    accepted for publication in Annals of Combinatorics (special issue in honor of George Andrews' 80th birthday), ArXiv
  4. Asymptotic Formulas Related to the $M_2$-rank of Partitions without Repeated Odd Parts (with D. Reihill)
    accepted for publication in The Ramanujan Journal ArXiv
  5. Peak Positions of Strongly Unimodal Sequences (with K. Bringmann, K. Mahlburg, and R. Rhoades)
    accepted for publication in Transactions of the American Mathematical Society ArXiv
  6. The Generating Function of the M2-rank of Partitions without Repeated Odd Parts as a Mock Modular Form
    Transactions of the American Mathematical Society, Vol. 371 Number 1, pages 249-277 (2019) ArXiv Maple File
  7. When Fourth Moments are Enough (with D. Skinner and E. Waymire),
    Rocky Mountain Journal of Mathematics, Vol. 48 Number 6, pages 1917--1924 (2018) ArXiv
  8. Mock modularity of the Md-rank of overpartitions (with H. Swisher)
    Journal of Mathematical Analysis and Applications, Vol. 466 Issue 2, pages 1144-1189 (2018) ArXiv
  9. On a modularity conjecture of Andrews, Dixit, Schultz, and Yee for a variation of Ramamunjan's ω(q) (with K. Bringmann and K. Mahlburg)
    Advances in Mathematics, Vol. 325, pages 505--532 (2018) ArXiv
  10. Some Smallest Parts Functions from Variations of Bailey's Lemma
    in Frontiers in Orthogonal Polynomials and q-Series, Chapter 18, pages 343-372 (2018) ArXiv
  11. Ranks For Two Partition Quadruple Functions
    Journal de Theorie de Nombres de Bordeaux, Vol. 29 number 2, pages 425-443 (2017) ArXiv
  12. Two Partition Functions with Congruences modulo 3, 5, 7, and 13
    Annals of Combinatorics, Vol. 21 number 3, (2017), pages 397-443 ArXiv
  13. Exotic Bailey-Slater SPT-Functions I: Group A
    Advances in Mathematics, Vol. 305, (2017), pages 479-514 ArXiv
  14. Higher Order Smallest Parts Functions and Rank-Crank Moment Inequalities from Bailey Pairs (with C. Babecki and G. Sangston)
    Research in Number Theory, Vol. 2(1), (2016), pages 1-35 ArXiv
  15. Exotic Bailey-Slater SPT-Functions II: Hecke-Rogers-Type Double Sums and Bailey Pairs From Groups A, C, E (with F. Garvan)
    Advances in Mathematics, Vol. 299, (2016), pages 605-639 ArXiv
  16. Exotic Bailey-Slater SPT-Functions III: Bailey Pairs from Groups B, F, G, and J
    Acta Arithmetica, Vol. 173 Number 4, (2016), pages 317-364, ArXiv
  17. Overpartition Rank Differences Modulo 7 by Maass Forms
    Journal of Number Theory, Vol. 163, (2016), pages 331-358, ArXiv
  18. Congruences for Partition Pairs with Conditions (formerly titled "Congruences for a Certain Partition Pair by a Crank"),
    Quarterly Journal of Mathematics, Vol. 66, No. 3 (2015), pages 837-860 ArXiv
  19. Rank and Crank Moments for Partitions without Repeated Odd Parts,
    International Journal of Number Theory, Vol. 11, No. 03 (2015), pages 683-703. Arxiv
  20. Higher Order SPT functions for overpartitions, overpartitions with smallest part even, and partitions without repeated odd parts
    Journal of Number Theory, Vol. 149, (2015), pages 285-312. ArXiv
  21. Another SPT crank for the number of smallest parts in overpartitions with even smallest part (formerly titled "Another proof of two modulo 3 congruences and another SPT crank for the number of smallest parts in overpartitions with even smallest part"),
    Journal of Number Theory, Vol. 148, (2015), pages 196-203. ArXiv
  22. The spt-crank for overpartitions (with F. Garvan),
    Acta Arithmetica, Vol. 166, No. 02 (2014), pages 141-188. ArXiv
  23. Hecke-type congruences for Andrews' spt-function modulo 16 and 32 (with F. Garvan),
    International Journal of Number Theory, Vol. 10, No. 02 (2014), pages 375-390. ArXiv
  24. A note on the transcendence of zeros of a certain family of weakly holomorphic modular forms (with H. Swisher),
    International Journal of Number Theory, Vol. 10, No. 02 (2014), pages 309-317.